| Euclides - 1864
...the remainder BG ; (ax. 3.) but it has been shewn that BCis equal to BG, wherefore AL and .BCare each **of them equal to BG; and things that are equal to the same** thing are equal to one another ; therefore the straight line AL is equal to BC. (ax. 1.) Wherefore... | |
| Francis Bacon - 1864
...whereas in distributive, if unequals be not given to unequals there is the greatest injustice.1 Again " **things that are equal to the same are equal to one another,"** is likewise a rule of mathematics ; but it is at the same time so potent in logic as to be the basis... | |
| Euclides - 1865
...the same thing are equal to one another ; therefore tne straight line AI. is equal to BC. (ax. 1.) **Wherefore from the given point A a straight line AL...has been drawn equal to the given straight line BC.** Which was to be done. PROP. III.— PROBLEM. From the greater of two given straight lines to cut off... | |
| Sir William Hamilton - 1866 - 530 sider
...certainly than through demonstration, that we know in a common notion.' .... Such common notions are—' **Things that are equal to the same are equal to one another,'—'** If equals be taken from equals the remainders are equal,'—' Every thing must be either affirmed or... | |
| Euclid, Isaac Todhunter - 1867 - 400 sider
...to BG. But things which are equal to the same thing are equal to one another. [Axiom 1 . Therefore **AL is equal to BC. "Wherefore from, the given point...has been drawn equal to the given straight line BC.** QEF PROPOSITION 3. PROBLEM. From the greater of two given straight lines to cut off a part equal to... | |
| Euclid, Isaac Todhunter - 1867 - 400 sider
...equal to BG. But things which are equal to the same thing are equal to one another. [Axiom 1. Therefore **AL is equal to BC. Wherefore from the given point A a straight line** AI, has been drawn equal to the given straight line BC. QEP PROPOSITION 3. PROBLEM. From the greater... | |
| Robert Potts - 1868 - 410 sider
...the remainder BG; (ax. 3.) but it has been shewn that .BCis equal to BG, wherefore AL and BCaie each **of them equal to BG; and things that are equal to the same** thing are equal to one another ; therefore the straight line AL is equal to BC. (ax. 1.) Wherefore... | |
| Euclid, Charles Peter Mason - 1872
...straight line, the adjacent £s so formed are together equal to two right £s. (Prop. XIII.) 2. That **things that are equal to the same are equal to one another.** (Ax. I.) 3. That if the same quantity be taken from two equal quantities the remainders are equal.... | |
| Henry Major - 1873
...equal to the remainder BG; but it has been shown that BC is equal to BG ; wherefore AL and BC are cash **of them equal to BG ; and things that are equal to the same are equal to one another ; therefore** AL is equal to BC. Wherefore from the given point A a straight line AL has been drawn equal to the... | |
| Euclides - 1874
...to BG ; and things which are equal to the same thing are equal to one another (Ax. 1) ; therefore 4. **The straight line AL is equal to BC. Wherefore, from...has been drawn equal to the given straight line BC.** Which was to be done. PROPOSITION 3. — Problem. From the greater of two given straight lines to cut... | |
| |